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What is the Least Common Multiple of 57132 and 57144?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 57132 and 57144 is 272062584.

LCM(57132,57144) = 272062584

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Least Common Multiple of 57132 and 57144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57132 and 57144, than apply into the LCM equation.

GCF(57132,57144) = 12
LCM(57132,57144) = ( 57132 × 57144) / 12
LCM(57132,57144) = 3264751008 / 12
LCM(57132,57144) = 272062584

Least Common Multiple (LCM) of 57132 and 57144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57132 and 57144. First we will calculate the prime factors of 57132 and 57144.

Prime Factorization of 57132

Prime factors of 57132 are 2, 3, 23. Prime factorization of 57132 in exponential form is:

57132 = 22 × 33 × 232

Prime Factorization of 57144

Prime factors of 57144 are 2, 3, 2381. Prime factorization of 57144 in exponential form is:

57144 = 23 × 31 × 23811

Now multiplying the highest exponent prime factors to calculate the LCM of 57132 and 57144.

LCM(57132,57144) = 23 × 33 × 232 × 23811
LCM(57132,57144) = 272062584